Direct Energy, 2018a

13 THOMAS FERMI ANALYSIS 297
Electron
cloud
Electron under
consideration
-
Nucleus
Figure 13.1: Illustration ofan atom.
To understand what happens when the electron is moved, consider the
energy ofthe atom in more detail. Coulomb's law, introduced in Eq.
1.4, tells us that charged objects exert forces on other charged objects.
More specically, the electric eld intensity −→ E due to a point charge of Q
coulombs a distance r away surrounded by a material with permittivity ɛ
is given by
−→ Qâ r E =
4πɛr . 2 (13.18)
The atom is composed of N positively charged protons. The electron under
consideration feels an attractive Coulomb force due to these protons. Additionally,
the atom has N electrons, and N − 1 ofthese exert a repulsive
Coulomb force on the electron under consideration. Since a charge separation
and electric eld exist, energy is stored. Call the component ofthe
energy ofthe atom due to the Coulomb interaction between the protons
ofthe nucleus and the electron under consideration E Coulomb e nucl . Call
the Coulomb interaction between the electron under consideration and all
other electrons E e e interact . The atom also has kinetic energy. Call the
kinetic energy ofthe nucleus E kinetic nucl and the kinetic energy ofall ofthe
electrons E kinetic e . The energy ofthe atom is the sum ofall ofthese terms.
E atom = E Coulomb e nucl. + E kinetic nucl + E e e interact + E kinetic e (13.19)
Energy due to spin ofthe electrons and protons is ignored as is energy due
to interaction with any other nearby charged objects. At T ≈ 0 K, the
kinetic energy ofthe nucleus will be close to zero, so we can ignore the
term, E kinetic nucl ≈ 0. The quantity E kinetic e cannot be exactly zero. In
Chapter 6 we plotted energy level diagrams for electrons around an atom.
Even at T =0K, electrons have some internal energy, and this energy is
denoted by the energy level occupied.